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We consider a generalization of a recently proposed non-Hermitian model for resonant cavities coupled by a chiral mirror by taking into account number non-conservation and nonlinear interactions. We analyze non-Hermitian quantum dynamics of populations and entanglement of the cavity modes. We find that the interplay between initial coherence and non-Hermitian coupling leads to a counterintuitive population transfer. While an initially coherent cavity mode is depleted, the other empty cavity can be populated more than or less than the initially filled one. Moreover, the presence of nonlinearity yields population collapse and revival as well as bipartite entanglement of the cavity modes. In addition to coupled cavities, we point out that similar models can be found in PT -symmetric Bose-Hubbard dimers of Bose-Einstein condensates or in coupled soliton-plasmon waveguides. We specifically illustrate the quantum dynamics of populations and entanglement in a heuristic model that we propose for a soliton-plasmon system with soliton amplitude-dependent asymmetric interaction. Degree of asymmetry, nonlinearity and coherence are examined to control plasmon excitations and soliton-plasmon entanglement. Relations to PT -symmetric lasers and Jahn-Teller systems are pointed out., Scientific and Technological Research Council of Turkey (TÜBİTAK); office of Vice President for Research and Development (VPRD) of Koç University; Department of Physics of the Koç University